Question

It is required to reduce the volume of a gas by 20% by compressing it at a constant pressure. To do so, the gas has to be cooled. If the gas attains a final temperature of 157°C, find the initial temperature of the gas.

Answer 1

Initial conditions:

V₁ = Initial volume of the gas = V

T₁ = Initial temperature of the gas = ?

Final conditions:

V₂ (Final volume) = reduce by 20%

= V - `20/100` of V

= `(80"V")/100`

= `(4"V")/5`

T₂ = Final temperature of the gas = 157°C = 157 + 273 = 430 K

By Charles Law:

`"V"_1/"T"_1 = "V"_2/"T"_2`

Substituting the values:

`"V"/"T"_1 = ((4"V")/5)/430`

`1/"T"_1 = 4/(5 xx 430)`

T₁ = `(430 xx 5)/4`

T₁ ​= 537.5 K

Therefore, final temperature of the gas = 537.5 K - 273 K = 264.5°C